Uncertainty Quantification (UQ) is an emerging and extremely active research discipline
which aims to quantitatively treat any uncertainty in applied models. The primary objective of …

We study the application of a tailored quasi-Monte Carlo (QMC) method to a class of optimal
control problems subject to parabolic partial differential equation (PDE) constraints under …

Topology optimization under uncertainty (TOuU) often defines objectives and constraints by
statistical moments of geometric and physical quantities of interest. Most traditional TOuU …

Models incorporating uncertain inputs, such as random forces or material parameters, have
been of increasing interest in PDE-constrained optimization. In this paper, we focus on the …

We consider an optimal control problem governed by an elliptic partial differential equation
(PDE) with random coefficient, and introduce an efficient numerical method for the problem …

In this paper, we focus on a numerical investigation of a strongly convex and smooth
optimization problem subject to a convection–diffusion equation with uncertain terms. Our …

For finite-dimensional problems, stochastic approximation methods have long been used to
solve stochastic optimization problems. Their application to infinite-dimensional problems is …

In this work, we present a novel approach for solving stochastic shape optimization
problems. Our method is the extension of the classical stochastic gradient method to infinite …

We consider a class of convex risk-neutral PDE-constrained optimization problems subject
to pointwise control and state constraints. Due to the many challenges associated with …

We study the nonlinear inverse problem of estimating stochastic parameters in the fourth-
order partial differential equation with random data. The primary focus is on developing a …